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In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems , where they simplify mathematical analysis by converting ...
In electrical engineering and control theory, a Bode plot / ˈ b oʊ d i / is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift.
Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) closer than it does other frequencies. It may cause violent swaying motions and potentially catastrophic failure in ...
ω 0 = k / m {\textstyle \omega _ {0}= {\sqrt {k/m}}} is called the undamped angular frequency of the oscillator or the natural frequency, ζ = c 2 m k {\displaystyle \zeta = {\frac {c} {2 {\sqrt {mk}}}}} is called the damping ratio. Many sources also refer to ω0 as the resonant frequency.
A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock.
Using the natural frequency of a harmonic oscillator = / and the definition of the damping ratio above, we can rewrite this as: d 2 x d t 2 + 2 ζ ω n d x d t + ω n 2 x = 0. {\displaystyle {\frac {d^{2}x}{dt^{2}}}+2\zeta \omega _{n}{\frac {dx}{dt}}+\omega _{n}^{2}x=0.}
The ultimate end goal is to meet requirements typically provided in the time-domain called the step response, or at times in the frequency domain called the open-loop response. The step response characteristics applied in a specification are typically percent overshoot, settling time, etc.
A second-order Butterworth filter (i.e., continuous-time filter with the flattest passband frequency response) has an underdamped Q = 1 ⁄ √ 2. [11] A pendulum's Q-factor is: Q = M ω / Γ {\textstyle Q={M\omega }/{\Gamma }} , where M is the mass of the bob, ω = 2π/ T is the pendulum's radian frequency of oscillation, and Γ is the ...
Bandwidth (signal processing) Amplitude (a) vs. frequency (f) graph illustrating baseband bandwidth. Here the bandwidth equals the upper frequency. Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in unit of hertz (symbol Hz).
The frequency response function (FRF) of any linear dynamic system composed of many coupled components will in general display distinctive resonance-antiresonance behavior when driven. [3] As a rule of thumb, it can be stated that as the distance between the driven component and the measured component increases, the number of antiresonances in ...